He died in Ashtead, Surrey. He had married professional musician Ada Mary Thomas in 1914; they had a son, Geoffrey Thomas Heath, and a daughter, Veronica Mary Heath. Heath's son Geoffrey went to Trinity College, Cambridge, before becoming a teacher at Ampleforth College and had 6 children.

Heath was distinguished for his work in Greek mathematics and was author of several books on Greek mathematicians. It is primarily through Heath's translations that modern English-speaking readers are aware of what Archimedes did. His translation of the celebrated Archimedes Palimpsest, however, was based on a transcription that had lacunae, which scholars such as Reviel Netz have been able to fill in to a certain extent, by exploiting scientific methods of imagery not available in Heath's time.

When Heath's Works of Archimedes was published in 1897, the Archimedes Palimpsest had not been extensively explored. Its significance was not recognised until 1906, when it was examined by Danish professor Johan Ludvig Heiberg. The palimpsest contained an extended version of Stomachion, and a treatise entitled The Method of Mechanical Theorems that had previously been thought lost. These works have been a focus of research by later scholars.